Likelihood profile for parameter alpha used in computation 

of statistical uncertainty for ERR/Sv in NIH-IREP lung 

cancer model; re: Table IV.D.3, page 50, Report of the NCICDC Working Group to Revise the 1985 NIH 

Radioepidemiological Tables 

(Personal communication from Dr. Charles Land, NCI) 

From: Land, Charles (NIH/NCI) [landc@exchange.nih.gov] 

Sent: Tuesday, February 03, 2004 3:02 PM 

To: Henshaw, Russell 

Subject: RE: Request for Pierce analysis 

Russ, the attachment is the amfit analysis Don Pierce sent me, giving 

the likelihood profile in Table IV.D.3 for parameter alpha. I copied 

the log file onto a Word document to retain the format. In the model, 

the variables in Linear term 1 and loglinear term 1 pertain to the 

modeled baseline risk; loglinear term 2 has the linear dose-response 

coefficient, in log scale (parameter 20) and fixed parameter values 

corresponding to the Model 2 conventions for plus minus 1/2 for sex, 

f(e) for exposure age, and g(a) for attained age. 

If it isn't crystal clear, give me a call. 

Charles 

ATTACHMENT 

USE C:\workrerf\smoking\final\smoklung.BSF 

 

BSF File created by AMFIT on October 24, 2000 12:31:00 pm 

Program information: 16 25 

Description: This BSF file generated by EPICURE 

 

INPUT @ 

Input from C:\workrerf\smoking\final\smoklung.BSF 

 39022 records read 39022 records used 

 0 records rejected 

 

37 variables defined At least 500 additional variables can be created. 

cases lung @ 

pyr apyr @ 

fitopt iter 70 @ 

CATEGORY agex AS ax7cat < / 10 (10) 60 > @ 

ax7cat has 7 levels from 1 to 7 

strata city sex ax7cat agecat @ 

 

The current model has 560 strata 

sele stopper==1 and smokcat>1 @ 

23460 records to be used 
2

 

tran fem=sex==2 ; e30sq=e30^2 ; e30cub=e30^3; sexvar=2*sex-3 @ 

tran lage50a=min(log(age/50),0); lage60a=min(log(age/60),0); 

lage70a=min(log(age/70),0)@ 

tran e30a15_30 = min(max(-15,e30),0) @ 

line 1 smokcat2 @ 

para 3=0 4:4.5 5:8.8 6:14 @ 

logl 1 acat fem sex*e30 sex*e30sq sex*e30cub @ 

para 7:-0.22 8:-1.6 9=0 10:-0.26 11:-0.52 13:-0.05 14:0.03 @ 

line 2 lun_ad10=1 @ 

 

logl 2 %con:0.5 sexvar e30a15_30 lage50a @ 

!fit @ null @ 

!prof 20 @ 

para 21 = 0.4215 @ 

para 22 = -.05255 @ 

para 23 = -1.626 @ 

fit @ 

 

 Iter Step Deviance 

 0 0 2937.541 

 1 0 2926.434 

 2 0 2923.116 

 3 0 2921.197 

 4 0 2919.809 

 5 0 2918.958 

 6 0 2918.472 

 7 0 2918.132 

 8 0 2917.876 

 9 0 2917.679 

 10 0 2917.522 

 11 0 2917.396 

 12 0 2917.292 

 13 0 2917.206 

 14 0 2917.135 

 15 0 2917.074 

 16 0 2917.022 

 17 0 2916.978 

 18 0 2916.941 

 19 0 2916.909 

 20 0 2916.881 

 21 0 2916.857 

 22 0 2916.836 

 23 0 2916.819 

 24 0 2916.804 

 25 0 2916.791 

 26 0 2916.780 

 27 0 2916.770 

 28 0 2916.762 

 29 0 2916.755 

 30 0 2916.750 

 31 0 2916.745 

 32 0 2916.741 
3

 33 0 2916.737 

 34 0 2916.734 

 35 0 2916.732 

 36 0 2916.729 

 37 0 2916.728 

 38 0 2916.726 

 39 0 2916.725 

 40 0 2916.724 

 41 0 2916.723 

 42 0 2916.722 

 43 0 2916.722 

 44 0 2916.721 

 45 0 2916.721 

 46 0 2916.721 

 47 0 2916.720 

 48 0 2916.720 

 49 0 2916.720 

 

Piece-wise exponential regression 

Product additive excess model { T0 * ( 1 + T1 + T2 + ...) } 

Stratification on CITY SEX ax7cat AGECAT with 229 strata 

 

Using stopper==1 and smokcat>1 

 LUNG is used for cases 

 APYR is used for person years 

 

 Parameter Summary Table 

 # Name Estimate Std.Err. Test Stat. P value 

-- ---------------------------- ---------- --------- ---------- -------- 

Linear term 1 

 2 SMOKCAT2_1............... 0.000 Aliased 

 3 SMOKCAT2_2............... 0.000 Fixed 0.06149 > 0.5 

 4 SMOKCAT2_3............... 4.057 2.106 1.927 0.054 

 5 SMOKCAT2_4............... 7.928 3.867 2.05 0.0404 

 6 SMOKCAT2_5............... 12.71 6.285 2.022 0.0432 

 

Log-linear term 1 

 7 ACAT_1................... -1.093 1.986 -0.5503 > 0.5 

 8 ACAT_2................... -1.726 1.007 -1.713 0.0867 

 9 ACAT_3................... 0.000 Aliased 

10 ACAT_4................... -0.2290 0.4361 -0.525 > 0.5 

11 ACAT_5................... -0.4688 0.5245 -0.8938 0.371 

12 fem...................... 0.1031 0.4885 0.211 > 0.5 

13 SEX_1 * E30.............. -0.04044 0.02992 -1.352 0.176 

14 SEX_2 * E30.............. 0.02250 0.0361 0.6234 > 0.5 

15 SEX_1 * e30sq............ 0.001027 0.001117 0.9195 0.358 

16 SEX_2 * e30sq............ -0.005169 0.003657 -1.413 0.158 

17 SEX_1 * e30cub........... 7.255e-05 4.748e-05 1.528 0.126 

18 SEX_2 * e30cub........... 0.0001941 0.000127 1.528 0.127 

 

Linear term 2 

19 LUN_AD10................. 1.000 Aliased 

 

Log-linear term 2 
4

20 %CON..................... -0.1505 0.2981 -0.5048 > 0.5 

21 SEXVAR................... 0.4215 Fixed 0.07885 > 0.5 

22 e30a15_30................ -0.05255 Fixed 0.5795 > 0.5 

23 lage50a.................. -1.626 Fixed -0.612 > 0.5 

 

 Records used 23460 

 Deviance 2916.72 

 Pearson Chi2 73679.46 Degrees of freedom 23216 

 

prof 20 @ 

 Upper bound trial values 

 Deviance One-Sided 

 Beta Change P-Value 

 ____________________________ 

 

 -0.09089 -0.03796 0.423 * 

 0.1635 -1.169 0.140 * 

 0.04680 -0.4398 0.254 * 

 0.1410 -0.9970 0.159 * 

 0.1824 -1.323 0.125 * 

 0.3156 -2.733 0.0491 * 

 0.3952 -3.865 0.0247 * 

 0.4645 -5.039 0.0124 * 

 0.5455 -6.649 0.00496 * 

 0.6001 -7.887 0.00249 * 

 

 Lower bound trial values 

 Deviance One-Sided 

 Beta Change P-Value 

 ____________________________ 

 

 -0.2101 -0.03436 0.426 * 

 -0.4975 -1.042 0.154 * 

 -0.3783 -0.4735 0.246 * 

 -0.4899 -1.001 0.159 * 

 -0.5449 -1.316 0.126 * 

 -0.7364 -2.644 0.0520 * 

 -0.8767 -3.783 0.0259 * 

 -1.013 -4.974 0.0129 * 

 -1.189 -6.575 0.00517 * 

 -1.327 -7.841 0.00255 * 

 

 Sorted list of profile likelihood points 

 Deviance One-Sided 

 Beta Change P-Value 

 ____________________________ 

 

 -1.327 -7.841 0.00255 

 -1.189 -6.575 0.00517 

 -1.013 -4.974 0.0129 

 -0.8767 -3.783 0.0259 
5

 -0.7364 -2.644 0.0520 

 -0.5449 -1.316 0.126 

 -0.4899 -1.001 0.159 

 -0.4975 -1.042 0.154 

 -0.3783 -0.4735 0.246 

 -0.2101 -0.03436 0.426 

 -0.1505 0.000 0.00 

 -0.09089 -0.03796 0.423 

 0.04680 -0.4398 0.254 

 0.1410 -0.9970 0.159 

 0.1635 -1.169 0.140 

 0.1824 -1.323 0.125 

 0.3156 -2.733 0.0491 

 0.3952 -3.865 0.0247 

 0.4645 -5.039 0.0124 

 0.5455 -6.649 0.00496 

 0.6001 -7.887 0.00249 

 

 Interpolated profile likelihood bounds 

 for parameter 20 (%CON) 

 

 MLE -0.1505 exp(MLE) 0.8603 

 2-sided Bounds exp(Bounds) 

 Level Lower Upper Lower Upper 

 _______________________________________________________ 

 

 25.0% -0.2547 -0.05451 0.7751 0.9470 

 50.0% -0.3735 0.04999 0.6883 1.051 

 68.3% -0.4899 0.1414 0.6127 1.152 

 75.0% -0.5461 0.1825 0.5792 1.200 

 90.0% -0.7445 0.3134 0.4750 1.368 

 95.0% -0.8836 0.3937 0.4133 1.483 

 97.5% -1.019 0.4637 0.3611 1.590 

 99.0% -1.196 0.5448 0.3025 1.724 

 99.5% -1.331 0.5998 0.2642 1.822 

 

0.9975 1.822 

0.995 1.724 

0.9875 1.590 

0.975 1.482 

0.95 1.368 

0.875 1.200 

0.8413 1.152 

0.75 1.051 

0.625 0.9469 

0.5 0.8603 

0.375 0.7751 

0.25 0.6883 

0.1587 0.6127 

0.125 0.5792 

0.05 0.4750 

0.025 0.4133 

0.0125 0.3610 

0.005 0.3024 

0.0025 0.2642